"We are excited to get these players in uniform and to see all the young talent that we recently drafted in action," said Tom McNamara, the director of amateur scouting.
Pryor, who attended Tennessee Tech University, went 4-4 with a 5.71 ERA in 24 outings this past season, including one start. The 6-foot-4, 235-pounder also had four saves for the Golden Eagles.
He holds the school record for strikeouts per nine innings with almost 16 1/2 and held opposing hitters to a .224 average.
Other Draft selections reaching contract agreements were infielder Daniel Lopez (16th), right-hander Willy Kesler (18th), outfielder Franklin Christian (19th) and right-hander Matt Bischoff (20th).